A caterpillar inside the webbed leaves. For Bt to work, the cat must eat the treated leaves.

Your critter looks like the larva of a butterfly. It COULD be of a moth but I think they usually have fuzzy caterpillars. I also have citrus and the butterfly larvae are common on my trees about this time of year. Sometimes I see one of the big black and yellow butterflies flying from leaf to leaf, probably laying eggs. The other pest I have is leaf miners which burrow around just under the lower surface of new leaves.

Depending on the caterpillar size, if this photo was taken in England it would probably be the larva of the Light Brown Apple Moth. It causes the exact damage you describe and it is also a known pest in parts of California. An introduction from Australia, my information and photos of larva and moth are at the link below.
There is also a research article at
http://link.springer.com/article/10.1007%2Fs10530-010-9725-8/fulltext.html

Here is a link that might be useful: Light Brown Apple Moth in UK

That sure looks like it. I am mixing up a neem oil / spinodad cocktail and going to town on my yard this weekend.

It's one of the many species of leaf rollers, the adults of which are moths. (John, not all moth larvae are fuzzy.)

Serge, be sure to read the directions on your neem. High temperatures can cause foliar damage.

Thanks, Rhizo, will do! It's